TEMPORAL DISCRETIZATION ERRORS IN NONITERATIVE SPLIT-OPERATOR APPROACHES TO SOLVING CHEMICAL-REACTION GROUNDWATER TRANSPORT MODELS

Split-operator approaches are methods in widespread use for numerical solutions of reaction/transport problems. However, only a couple of an alyses of truncation errors resulting from operator splitting have bee n published. A range of linear, single species models is analysed here , leading to generalisations of earlier findings, in addition to devel oping new results. Linear retardation, radioactive decay and interphas e mass transfer are considered in detail. Operator-splitting errors fo r both the standard two-step and alternating two-step methods are pres ented, the latter approach being popular as a way to reduce errors due to operator splitting. An ambiguity in implementing two-step methods is revealed. The truncation error analysis also shows that the applica tion of the usual alternating split-operator method to an equilibrium reaction (linear retardation) actually increases the (first order in t ime) truncation error relative to the standard method. However, for ho mogeneous boundary conditions, the same reaction can be solved to seco nd-order accuracy if the model derived from taking the limit of a none quilibrium, interphase mass transfer process is used. For the linear r eactions considered here, the alternating two-step method is always se cond-order accurate in the temporal discretisation.